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w1 - Rob Bayer Instructions Math 55 Math 55 Worksheet Logic...

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Rob Bayer Math 55 Worksheet August 30, 2010 Instructions Introduce yourselves! Despite popular belief, math is in fact a team sport! Find some blackboard space, a piece of chalk, and decide who will be your ±rst scribe. Do the problems below, having a di²erent person be the scribe for each one. Try to work out the problems as a group, but feel free to ³ag me down if you run into a wall. Logic Symbols and Truth Tables 1. Let c =“It is cloudy,” r =“It is raining”, s =“It is sunny”, w =“The ground is wet”, n = “It is night”. Translate each of the following into English (a) c →¬ s (b) ¬ s c n (c) r w c 2. Using the same propositional variables as above, translate each of the following into formal logical statements: (a) It is raining whenever the ground is wet. (b) If it’s sunny, then it’s not raining. (c) It only rains at night. 3. Create a truth table for each of the following expressions. Determine whether each is a tautology, a contradiction, or neither. (a) ( p q ) ( ¬ p q ) (b) p q p q (c) p ( ¬ p q ) (d) ¬ ( p q ) ↔¬ p ∨¬ q Logic Puzzles 1. The island of Knights and Knaves has only two kinds of inhabitants: Knights (who always tell the truth) and Knaves (who always lie). After being shipwrecked on the island, you decide to try to ±gure out who the
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